Submitted by 
Gerrit Oomens 
Date 
01011900 
Reference 
JeanPierre Serre Letter to G. van der Geer September 1, 1997.

Comments


Tags 
Methods from general class field theory 
User comments
Correction

S.E.Fischer
12202014 03:42

The extension E/F leads to a curve of genus 4 with 8 points. Extending once again by H of degree 2 leads to the desired result, as we write
H/(E/F):= v^2 + v + x^3 + x .

Explicit Curve

S.E.Fischer
12182014 15:30

We can assume such a curve C as an extension E of degree 2 of a curve F of genus 1 as follows:
F: (x + y + x*y) * x*y + x + 1 ;
E/F := v^2 + v + x^3 + x .

Defining equation

Isabel Pirsic
06182012 13:00

(x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*y^8 +
(x^10 + x^9 + x^6 + x^5 + x + 1)*y^4 +
(x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2)*y^2 +
(x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5)*y +
x^21 + x^20 + x^17 + x^15 + x^11 + x^10 + x^8 + x^6


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